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Izvestiya: Mathematics, 2010, Volume 74, Issue 4, Pages 805–817
DOI: https://doi.org/10.1070/IM2010v074n04ABEH002508 (Mi im3989) 		 
This article is cited in 17 scientific papers (total in 17 papers)

On polynomial integrals of a mechanical system on a two-dimensional torus

A. E. Mironovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University, Mechanics and Mathematics Department
English version PDF (214 kB) Citations (17)
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DOI: https://doi.org/10.1070/IM2010v074n04ABEH002508
Abstract: We shall show that if a natural mechanical system defined on a two-dimensional torus and having a real analytic potential possesses a polynomial integral of odd degree in momenta, then the leading coefficients in the momenta satisfy two identities of a special form. We also show that if the system possesses an integral of the fifth degree in momenta, then there exists an integral of the first degree in momenta.
Keywords: integrable Hamiltonian system, polynomial integral.
Received: 04.09.2008
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2010, Volume 74, Issue 4, Pages 145–156
DOI: https://doi.org/10.4213/im3989
Bibliographic databases:
Document Type: Article
UDC: 517.938
MSC: 37J35, 37J99, 37K10, 53C80, 70G10, 70H03, 70H05, 70H06, 70H25
Language: English
Original paper language: Russian
Citation: A. E. Mironov, “On polynomial integrals of a mechanical system on a two-dimensional torus”, Izv. RAN. Ser. Mat., 74:4 (2010), 145–156; Izv. Math., 74:4 (2010), 805–817
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:282
    English version PDF:52
    References:90
    First page:18
     
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